In analogue of spherical harmonics, we have shown in [1]}, [2]} that on the surface of the cone and the
hyperboloid, orthogonal polynomials of degree \(n\)  or those that are even in \(t\)  variable of degree \(n\)  are
eigenfunctions of a second order differential operator with eigenvalues depending only on \(n\) . This important
property, however, does not hold for the paraboloid. The best we can do is the following proposition.
